3-1 Forecasting

William J. Stevenson

Operations Management

8th edition

3-2 Forecasting

CHAPTER3

Forecasting

McGraw-Hill/IrwinOperations Management, Eighth Edition, by William J. StevensonCopyright © 2005 by The McGraw-Hill Companies, Inc. All rights

reserved.

3-3 Forecasting

FORECAST: A statement about the future value of a variable of interest such

as demand. Forecasts affect decisions and activities throughout an

organization Accounting, finance Human resources Marketing MIS Operations Product / service design

3-4 Forecasting

Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads

Product/service design New products and services

Uses of ForecastsUses of Forecasts

3-5 Forecasting

Assumes causal systempast ==> future

Forecasts rarely perfect because of randomness

Forecasts more accurate forgroups vs. individuals

Forecast accuracy decreases as time horizon increases I see that you will

get an A this semester.

3-6 Forecasting

Elements of a Good ForecastElements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

l

Written

Easy

to u

se

3-7 Forecasting

Steps in the Forecasting ProcessSteps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Establish a time horizon

Step 3 Select a forecasting technique

Step 4 Gather and analyze data

Step 5 Prepare the forecast

Step 6 Monitor the forecast

“The forecast”

3-8 Forecasting

Types of ForecastsTypes of Forecasts

Judgmental - uses subjective inputs

Time series - uses historical data assuming the future will be like the past

Associative models - uses explanatory variables to predict the future

3-9 Forecasting

Judgmental ForecastsJudgmental Forecasts

Executive opinions Sales force opinions Consumer surveys Outside opinion Delphi method

Opinions of managers and staff Achieves a consensus forecast

3-10 Forecasting

Time Series ForecastsTime Series Forecasts

Trend - long-term movement in data Seasonality - short-term regular variations in

data Cycle – wavelike variations of more than one

year’s duration Irregular variations - caused by unusual

circumstances Random variations - caused by chance

3-11 Forecasting

Forecast VariationsForecast Variations

Trend

Irregularvariation

Seasonal variations

908988

Figure 3.1

Cycles

3-12 Forecasting

Naive ForecastsNaive Forecasts

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

The forecast for any period equals the previous period’s actual value.

3-13 Forecasting

Simple to use Virtually no cost Quick and easy to prepare Data analysis is nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy

Naïve ForecastsNaïve Forecasts

3-14 Forecasting

Stable time series data F(t) = A(t-1)

Seasonal variations F(t) = A(t-n)

Data with trends F(t) = A(t-1) + (A(t-1) – A(t-2))

Uses for Naïve ForecastsUses for Naïve Forecasts

3-15 Forecasting

Techniques for AveragingTechniques for Averaging

Moving average

Weighted moving average

Exponential smoothing

3-16 Forecasting

Moving AveragesMoving Averages

Moving average – A technique that averages a number of recent actual values, updated as new values become available.

Weighted moving average – More recent values in a series are given more weight in computing the forecast.

MAn = n

Aii = 1n

3-17 Forecasting

Simple Moving AverageSimple Moving Average

MAn = n

Aii = 1n

35

37

39

41

43

45

47

1 2 3 4 5 6 7 8 9 10 11 12

Actual

MA3

MA5

3-18 Forecasting

Exponential SmoothingExponential Smoothing

• Premise--The most recent observations might have the highest predictive value.

Therefore, we should give more weight to the more recent time periods when forecasting.

Ft = Ft-1 + (At-1 - Ft-1)

3-19 Forecasting

Exponential SmoothingExponential Smoothing

Weighted averaging method based on previous forecast plus a percentage of the forecast error

A-F is the error term, is the % feedback

Ft = Ft-1 + (At-1 - Ft-1)

3-20 Forecasting

Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92

Example 3 - Exponential SmoothingExample 3 - Exponential Smoothing

3-21 Forecasting

Picking a Smoothing ConstantPicking a Smoothing Constant

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12

Period

Dem

and .1

.4

Actual

3-22 Forecasting

Common Nonlinear TrendsCommon Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3.5

3-23 Forecasting

Linear Trend EquationLinear Trend Equation

Ft = Forecast for period t t = Specified number of time periods a = Value of Ft at t = 0 b = Slope of the line

Ft = a + bt

0 1 2 3 4 5 t

Ft

3-24 Forecasting

Calculating a and bCalculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b t

n

3-25 Forecasting

Linear Trend Equation ExampleLinear Trend Equation Example

t yW e e k t 2 S a l e s t y

1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5

t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5

3-26 Forecasting

Linear Trend CalculationLinear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)

5 =

b = 5 (2499) - 15(812)

5(55) - 225 =

12495-12180

275 -225 = 6.3

143.5

3-27 Forecasting

Associative ForecastingAssociative Forecasting

Predictor variables - used to predict values of variable interest

Regression - technique for fitting a line to a set of points

Least squares line - minimizes sum of squared deviations around the line

3-28 Forecasting

Linear Model Seems ReasonableLinear Model Seems Reasonable

A straight line is fitted to a set of sample points.

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 15

14 2515 2716 2412 2014 2720 4415 347 17

Computedrelationship

3-29 Forecasting

Forecast AccuracyForecast Accuracy

Error - difference between actual value and predicted value

Mean Absolute Deviation (MAD) Average absolute error

Mean Squared Error (MSE) Average of squared error

Mean Absolute Percent Error (MAPE)

Average absolute percent error

3-30 Forecasting

MAD, MSE, and MAPEMAD, MSE, and MAPE

MAD = Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

MAPE = Actual forecas

t

n

/ Actual*100)

3-31 Forecasting

Example 10Example 10

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 215 2 2 4 0.922 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89

-2 22 76 10.26

MAD= 2.75MSE= 10.86

MAPE= 1.28

3-32 Forecasting

Controlling the ForecastControlling the Forecast

Control chart A visual tool for monitoring forecast errors Used to detect non-randomness in errors

Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are

present

3-33 Forecasting

Sources of Forecast errorsSources of Forecast errors

Model may be inadequate Irregular variations Incorrect use of forecasting technique

3-34 Forecasting

Tracking SignalTracking Signal

Tracking signal = (Actual-forecast)

MAD

•Tracking signal

–Ratio of cumulative error to MAD

Bias – Persistent tendency for forecasts to beGreater or less than actual values.

3-35 Forecasting

Choosing a Forecasting TechniqueChoosing a Forecasting Technique

No single technique works in every situation Two most important factors

Cost Accuracy

Other factors include the availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon

3-36 Forecasting

Exponential SmoothingExponential Smoothing

3-37 Forecasting

Linear Trend EquationLinear Trend Equation

3-38 Forecasting

Simple Linear RegressionSimple Linear Regression